Tear up the bread roll and put in a bowl. Cover with cold water and leave to soften for 15 minutes.
Beat one of the garlic cloves and a little salt and pepper into the mayonnaise and transfer to a small serving dish. Set aside.
Squeeze all the water out of the bread and put the bread in a food processor with the onion, remaining garlic, minced beef, egg and oregano. Season with salt and pepper, and process briefly to mix. Add the olives and process until they are chopped into the mixture. Shape into 4 even-sized burgers and place on the upper rack of the halogen oven. Brush with oil.
Set the temperature to 200°C (392°F) and grill the burgers for 15 minutes, turning once halfway through cooking, until cooked through.
Cut 4 slices, each about 1 cm (½ inch) thick, from the tomato and place a slice over each burger. Arrange the anchovies on top and cook for a further 1 minute. Serve with the garlic mayonnaise and a leafy salad.